Maths and Statistics Foundations Project
Group N
06/10/2017
1. Introduction
<<<<<<< HEADDiscrimination has long been a controversial topic. Forms of discrimination can range greatly but over the last few decades, one notable form of discrimination has been the phenomenon of an income gap that has existed in society (Blinder, 1973). A widely discussed form of this discrepancy in income is gender. The European Commission defines gender pay gap as “the difference between men“s and women“s pay, based on the average difference in gross hourly earnings of all employees“ (European Commission, 2017). In recent years especially, addressing the gender-related pay gap has been a policy matter of many countries namely those belonging to the EU (European Union, 2014).
=======Discrimination has long been a controversial topic. Forms of discrimination can range greatly but over the last few decades, one notable form of discrimination has been the phenomenon of an income gap that has existed in society (Blinder, 1973). A widely discussed form of this discrepancy in income is gender. The European Commission defines gender pay gap as “the difference between men“s and women“s pay, based on the average difference in gross hourly earnings of all employees“ (European Commission, 2017). In recent years especially, addressing the gender-related pay gap has been a policy matter of many countries namely those belonging to the EU (European Union, 2014).
>>>>>>> 27d27b978d441b867bd2eaeb638b4acc287e9ee0According to the United Nations (2017), there are aims to alleviate the issue of gender discrimination to ensure gender equality. The European Commission (2017) does state that gender discrimination is prohibited under European law. However, the Office for National Statistics (2017) states that female full-time employees in the UK earn on average 9.4 percent less than male full-time employees in 2016. This raises the question if gender pay discrimination currently exists in the UK, and or if there are other drivers affecting the differences in salary levels.
Consequently, this report aims to identify if pay discrimination currently exists in the United Kingdom. To examine this, we will use data from the Office of National Statistics Quarterly Labour Force Survey for the period of January to March 2017 (ONS, 2017). We will consider factors which may affect the pay gap such as differences in where and how people in the UK tend to work/[namely nature (e.g. ethnicity) and nurture factors (occupation, region of work). Following investigation of the variables and linear regressions, we hope to make inferences that would aid policy creation that aims to minimise the pay gap.
2. Theory
note: What do you expect to find?
Our null hypothesis is that all the predictors will not have a significant effect on salary. The alternative hypothesis is that the predictors do have a significant effect on salary.
We are interested in investigating whether this apparent income gap is a result of actual gender discrimination, which would be in accordance with our resources, or whether this phenomenon arises as a result of other variables’ influences. We will thus investigate it in a linear regression model with relevant variables.
In that aspect, we want to determine other possible causes of the income gap and whether working in different industry sectors or having different educational qualifications can affect salary when included in a linear regression model with salary as the independent variable.
(OR Our theory is that we believe, in line with our resources, that gender discrimination is still present in today’s society. This will mean that in theory, we will expect that gender will have an effect on salary.)
3. Methods
Our research into the dataset uses various statistical tools in R. Ggplot and knitr libraries were used to help visualise the data, dplyr was used for ease of data manipulation and lmtest was used to further our statistical research.
## Warning: package 'lmtest' was built under R version 3.4.23.1 Data Description
<<<<<<< HEADThe dataset initially consisted of 88,528 observations of 739 variables. In order to examine the relationship between salary and gender and explore the possibility of gender discrimination in the UK, we have selected variables which also may impact the pay gap. Our final dataset contains 570 observations of 7 variables. These are outlined below.
| Variable | Description | Further info |
|---|---|---|
Salary |
Salary of respondent (249.5 - 48000.0) | N.b. adjusted for inflation |
Age |
Age of respondent (0-99) | |
Sex |
Gender of respondent | |
Occupation |
Major occupation group of respondent | |
Industry |
Industry sector in main job | 1= Distribution, hotels, restaurants |
| 2 = Banking, Finance | ||
Education |
Highest qualification level | |
NumEmployee |
Number of employees at workplace | |
Religion |
Religion GB level | |
MaritalStatus |
Marital status | |
Ethnicity |
Ethnicity of respondent in GB | <<<<<<< HEAD =======>>>>>>> 27d27b978d441b867bd2eaeb638b4acc287e9ee0 |
Region of workplace |
Region of place of work |
For ease of analysis we manipulated certain variables. Salary was converted from intervals to continuous data, to allow for a linear regression with Salary as the dependent variable, and all other variables were condensed to a set number of dummy variables.
ADD DUMMY INFO?
>>>>>>> 27d27b978d441b867bd2eaeb638b4acc287e9ee0summary(facQlfs)## Age Sex Industry
## Min. :16.0 Male :262 Distribution, hotels, restaurants:111
## 1st Qu.:30.0 Female:281 Banking, Finance : 82
## Median :43.0 Public admin, education, health :203
## Mean :42.1 Other :147
## 3rd Qu.:53.0
## Max. :77.0
##
## Education NumEmployee
## Degree :164 Under 50 :268
## Higher Education: 51 Under 500:183
## A Level :115 Over 500 : 92
## GCSE A*-C :127
## Other : 52
## No : 34
##
## Occupation Salary
## Professional :105 Min. : 249.5
## Caring, Leisure, Other Service : 75 1st Qu.:10499.5
## Associate Professional, Technical : 66 Median :18499.5
## Administrative, Secretarial : 61 Mean :20860.0
## Managers, Directors, Senior Officials: 55 3rd Qu.:30499.5
## Sales, Customer Service : 53 Max. :48000.0
## (Other) :128
## Marital Religion Ethnicity workRegion
## Single :213 No :208 White:486 South East :121
## Married:268 Yes:335 Asian: 21 Yorkshire and the Humber: 96
## Other : 62 Black: 15 London : 91
## Other: 21 South West : 67
## North East : 54
## West Midlands : 47
## (Other) : 67| Industry Type | #Individuals |
|---|---|
| Distribution, hotels, restaurants | 111 |
| Banking, Finance | 82 |
| Public admin, education, health | 203 |
| Other | 147 |
| Education Type | #Individuals |
|---|---|
| Degree | 164 |
| Higher Education | 51 |
| A Level | 115 |
| GCSE A*-C | 127 |
| Other | 52 |
| No | 34 |
| Number of Employees | #Individuals |
|---|---|
| Under 50 | 268 |
| Under 500 | 183 |
| Over 500 | 92 |
| Occupation type | #Individuals |
|---|---|
| Managers, Directors, Senior Officials | 55 |
| Professional | 105 |
| Associate Professional, Technical | 66 |
| Administrative, Secretarial | 61 |
| Skilled Trades | 47 |
| Caring, Leisure, Other Service | 75 |
| Sales, Customer Service | 53 |
| Process, Plant, Machine Operatives | 31 |
| Elementary | 50 |
| Marital status | #Individuals |
|---|---|
| Single | 213 |
| Married | 268 |
| Other | 62 |
| Religion Type | #Individuals |
|---|---|
| No | 208 |
| Yes | 335 |
| Ethnicity Type | #Individuals |
|---|---|
| White | 486 |
| Asian | 21 |
| Black | 15 |
| Other | 21 |
| Regions of Workplace | #Individuals |
|---|---|
| White | 486 |
| Asian | 21 |
| Black | 15 |
| Other | 21 |
3.2 Strength and limitations
4. Analysis
4.1 Descriptive statistics
4.1.1 Univariate descriptive of variables
<<<<<<< HEADSex
- central tendency (mean, mode, median)
- dispersion (range, variance, maximum, minimum, quartiles & IQR, std.)
- frequency distribution tables
- bar charts
- histograms
Sex
man <- c(415, 532, 686, 773, 764, 757, 749, 656, 621)
woman <- c(366, 492, 573, 613, 568, 557, 529, 518, 405)
ages <- c("21-25", "26-30", "31-35", "36-40", "41-45", "46-50", "51-55", "56-60", "60-65")
dtmw <- data.frame(ages, man, woman)
ggplot(dtmw) +geom_line(aes(x= ages, y=man,col='male'),group=1)+geom_point(aes(x= ages, y=man,col='male'))+ geom_line(aes(x= ages, y=woman,col='female'),group=2) + geom_point(aes(x= ages, y=woman,col='female'))+ylim(0,800)+ scale_color_discrete(name='Sex')+labs(title='Mean gross weekly pays in main job',x='Age',y='Salary')+theme(plot.title=element_text(hjust=0.5))
## Don't know how to automatically pick scale for object of type labelled. Defaulting to continuous.
sextable<- facQlfs %>% select(Sex,Salary) %>% group_by(Sex) %>% summarise(Mean=mean(Salary),'Standard Deviation'=sd(Salary))
kable(sextable,align='l')| Sex | Mean | Standard Deviation |
|---|---|---|
| Male | 25812.52 | 12614.71 |
| Female | 16242.32 | 10833.12 |
Industry
## Don't know how to automatically pick scale for object of type labelled. Defaulting to continuous.
industrytable <- facQlfs %>% select(Industry,Salary) %>% group_by(Industry) %>% summarise(Mean=mean(Salary),'Standard Deviation'=sd(Salary))
kable(industrytable,align='l')| Industry | Mean | Standard Deviation |
|---|---|---|
| Distribution, hotels, restaurants | 13894.55 | 9311.661 |
| Banking, Finance | 25477.55 | 14122.353 |
| Public admin, education, health | 18955.17 | 11926.377 |
| Other | 26174.29 | 11810.261 |
Highest Education Level
MAYBE REMOVE BELOW
ggplot(facQlfs, aes(x=Occupation,fill=Education))+ geom_bar(position=position_dodge())+ labs(title='Highest Education Qualification distribution by Occupation',x='Occupation',y='Count')+ theme(plot.title = element_text(hjust = 0.5),axis.text = element_text(angle= 50, hjust = 0.9,size=6))
ggplot(facQlfs, aes(x=Education,fill=Occupation))+ geom_bar(position=position_dodge())+ labs(title='Occupation distribution among Highest Education Qualification',x='Occupation',y='Count')+ theme(plot.title = element_text(hjust = 0.5),axis.text = element_text(angle= 45, hjust = 0.9))
Highest Education Level
<<<<<<< HEAD
MAYBE REMOVE BELOW
ggplot(facQlfs, aes(x=Occupation,fill=Education))+ geom_bar(position=position_dodge())+ labs(title='Highest Education Qualification distribution by Occupation',x='Occupation',y='Count')+ theme(plot.title = element_text(hjust = 0.5),axis.text = element_text(angle= 50, hjust = 0.9,size=6))
ggplot(facQlfs, aes(x=Education,fill=Occupation))+ geom_bar(position=position_dodge())+ labs(title='Occupation distribution among Highest Education Qualification',x='Occupation',y='Count')+ theme(plot.title = element_text(hjust = 0.5),axis.text = element_text(angle= 45, hjust = 0.9))
## # A tibble: 6 x 2
## Education `mean(Salary)`
## <fctr> <dbl>
## 1 Degree 27478.49
## 2 Higher Education 20436.90
## 3 A Level 19052.11
## 4 GCSE A*-C 17511.61
## 5 Other 15926.26
## 6 No 15737.79## # A tibble: 9 x 2
## Occupation percent
## <fctr> <dbl>
## 1 Managers, Directors, Senior Officials 14.4508671
## 2 Professional 45.6647399
## 3 Associate Professional, Technical 13.2947977
## 4 Administrative, Secretarial 8.0924855
## 5 Skilled Trades 0.5780347
## 6 Caring, Leisure, Other Service 5.7803468
## 7 Sales, Customer Service 4.0462428
## 8 Process, Plant, Machine Operatives 1.1560694
## 9 Elementary 1.7341040eductable<- facQlfs %>% select(Education,Salary) %>% group_by(Education) %>% summarise(Mean=mean(Salary),'Standard Deviation'=sd(Salary))
kable(eductable,digits = 0, align=c('l','c','r'), caption = 'Salary Mean and Standard Deviation by Education')| Education | Mean | Standard Deviation |
|---|---|---|
| Degree | 27478 | 13489 |
| Higher Education | 20437 | 12662 |
| A Level | 19052 | 11375 |
| GCSE A*-C | 17512 | 11227 |
| Other | 15926 | 9723 |
| No | 15738 | 8761 |
Employee Numbers in workplace
## Don't know how to automatically pick scale for object of type labelled. Defaulting to continuous.
numemploytable<- facQlfs %>% select(NumEmployee,Salary) %>% group_by(NumEmployee) %>% summarise(Mean=mean(Salary),'Standard Deviation'=sd(Salary))
kable(numemploytable,digits = 0, align=c('l','l','r'), caption = 'Salary Mean and Standard Deviation by # of Employees')| NumEmployee | Mean | Standard Deviation |
|---|---|---|
| Under 50 | 18305 | 11951 |
| Under 500 | 20966 | 12002 |
| Over 500 | 28092 | 13217 |
Occupations
## Don't know how to automatically pick scale for object of type labelled. Defaulting to continuous.
occuptable<- facQlfs %>% select(Occupation,Salary) %>% group_by(Occupation) %>% summarise(Mean=mean(Salary),'Standard Deviation'=sd(Salary))
kable(occuptable,digits = 0, align='l', caption = 'Salary Mean and Standard Deviation by Occupation')| Occupation | Mean | Standard Deviation |
|---|---|---|
| Managers, Directors, Senior Officials | 30682 | 11546 |
| Professional | 29018 | 12956 |
| Associate Professional, Technical | 25735 | 12872 |
| Administrative, Secretarial | 17732 | 10511 |
| Skilled Trades | 22152 | 10931 |
| Caring, Leisure, Other Service | 13442 | 8217 |
| Sales, Customer Service | 11954 | 6063 |
| Process, Plant, Machine Operatives | 18488 | 8791 |
| Elementary | 11130 | 6786 |
Religion
Ethnicity
Region of Workplace
4.1.2 Bivariate descriptive
occupation industry occupation education
4.2 Correlation analyses
occupation industry occupation education
##
## Pearson's product-moment correlation
##
## data: qlfs$Education and qlfs$Occupation
## t = 14.009, df = 541, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.4513880 0.5751126
## sample estimates:
## cor
## 0.5159359##
## Pearson's product-moment correlation
##
## data: qlfs$Industry and qlfs$Occupation
## t = -5.2834, df = 541, p-value = 1.841e-07
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3000600 -0.1399736
## sample estimates:
## cor
## -0.22150874.3 Hypothesis tests
4.3.1 T-tests
##
## Welch Two Sample t-test
##
## data: caring$Salary and sales$Salary
## t = 1.1784, df = 125.74, p-value = 0.2409
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -1010.806 3986.058
## sample estimates:
## mean of x mean of y
## 13441.95 11954.32##
## Welch Two Sample t-test
##
## data: caring$Salary and elem$Salary
## t = 1.7133, df = 117.36, p-value = 0.08929
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -360.4099 4984.9032
## sample estimates:
## mean of x mean of y
## 13441.95 11129.70##
## Welch Two Sample t-test
##
## data: sales$Salary and elem$Salary
## t = 0.64894, df = 98.141, p-value = 0.5179
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -1697.030 3346.272
## sample estimates:
## mean of x mean of y
## 11954.32 11129.70##
## Pairwise comparisons using t tests with pooled SD
##
## data: facQlfs$Salary and facQlfs$Education
##
## Degree Higher Education A Level GCSE A*-C Other
## Higher Education 0.0026 - - - -
## A Level 1.2e-07 1.0000 - - -
## GCSE A*-C 5.8e-11 0.9639 1.0000 - -
## Other 2.6e-08 0.5435 0.9252 1.0000 -
## No 2.6e-06 0.6690 0.9639 1.0000 1.0000
##
## P value adjustment method: holm##
## Pairwise comparisons using t tests with pooled SD
##
## data: facQlfs$Salary and facQlfs$Sex
##
## Male
## Female <2e-16
##
## P value adjustment method: holm##
## Pairwise comparisons using t tests with pooled SD
##
## data: facQlfs$Salary and facQlfs$Industry
##
## Distribution, hotels, restaurants
## Banking, Finance 1.9e-10
## Public admin, education, health 0.0006
## Other 5.4e-15
## Banking, Finance
## Banking, Finance -
## Public admin, education, health 8.2e-05
## Other 0.6680
## Public admin, education, health
## Banking, Finance -
## Public admin, education, health -
## Other 9.9e-08
##
## P value adjustment method: holm##
## Pairwise comparisons using t tests with pooled SD
##
## data: facQlfs$Salary and facQlfs$NumEmployee
##
## Under 50 Under 500
## Under 500 0.023 -
## Over 500 2.2e-10 1.2e-05
##
## P value adjustment method: holm##
## Pairwise comparisons using t tests with pooled SD
##
## data: facQlfs$Salary and facQlfs$Occupation
##
## Managers, Directors, Senior Officials
## Professional 1.00000
## Associate Professional, Technical 0.12280
## Administrative, Secretarial 2.2e-09
## Skilled Trades 0.00097
## Caring, Leisure, Other Service < 2e-16
## Sales, Customer Service < 2e-16
## Process, Plant, Machine Operatives 8.6e-06
## Elementary < 2e-16
## Professional
## Professional -
## Associate Professional, Technical 0.37886
## Administrative, Secretarial 1.8e-09
## Skilled Trades 0.00395
## Caring, Leisure, Other Service < 2e-16
## Sales, Customer Service < 2e-16
## Process, Plant, Machine Operatives 2.9e-05
## Elementary < 2e-16
## Associate Professional, Technical
## Professional -
## Associate Professional, Technical -
## Administrative, Secretarial 0.00043
## Skilled Trades 0.52338
## Caring, Leisure, Other Service 3.5e-10
## Sales, Customer Service 1.1e-10
## Process, Plant, Machine Operatives 0.02619
## Elementary 1.5e-11
## Administrative, Secretarial
## Professional -
## Associate Professional, Technical -
## Administrative, Secretarial -
## Skilled Trades 0.27701
## Caring, Leisure, Other Service 0.20136
## Sales, Customer Service 0.05004
## Process, Plant, Machine Operatives 1.00000
## Elementary 0.01805
## Skilled Trades
## Professional -
## Associate Professional, Technical -
## Administrative, Secretarial -
## Skilled Trades -
## Caring, Leisure, Other Service 0.00022
## Sales, Customer Service 3.7e-05
## Process, Plant, Machine Operatives 0.79574
## Elementary 8.6e-06
## Caring, Leisure, Other Service
## Professional -
## Associate Professional, Technical -
## Administrative, Secretarial -
## Skilled Trades -
## Caring, Leisure, Other Service -
## Sales, Customer Service 1.00000
## Process, Plant, Machine Operatives 0.25016
## Elementary 1.00000
## Sales, Customer Service
## Professional -
## Associate Professional, Technical -
## Administrative, Secretarial -
## Skilled Trades -
## Caring, Leisure, Other Service -
## Sales, Customer Service -
## Process, Plant, Machine Operatives 0.08056
## Elementary 1.00000
## Process, Plant, Machine Operatives
## Professional -
## Associate Professional, Technical -
## Administrative, Secretarial -
## Skilled Trades -
## Caring, Leisure, Other Service -
## Sales, Customer Service -
## Process, Plant, Machine Operatives -
## Elementary 0.03473
##
## P value adjustment method: holm4.3.2 Chi-square tests
## Warning in chisq.test(table(facQlfs$Industry, facQlfs$Occupation)): Chi-
## squared approximation may be incorrect##
## Pearson's Chi-squared test
##
## data: table(facQlfs$Industry, facQlfs$Occupation)
## X-squared = 352.87, df = 24, p-value < 2.2e-16## Warning in chisq.test(table(facQlfs$Education, facQlfs$Occupation)): Chi-
## squared approximation may be incorrect##
## Pearson's Chi-squared test
##
## data: table(facQlfs$Education, facQlfs$Occupation)
## X-squared = 252.74, df = 40, p-value < 2.2e-164.4 Linear regression
##
## Call:
## lm(formula = Salary ~ Education + Sex + Industry + NumEmployee +
## Occupation + Marital + Religion + Ethnicity + workRegion,
## data = facQlfs)
##
## Residuals:
## Min 1Q Median 3Q Max
## -26967.0 -5948.4 505.5 5967.2 27261.8
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) 29672.0 2358.8 12.579
## EducationHigher Education -4026.8 1545.4 -2.606
## EducationA Level -4842.3 1326.3 -3.651
## EducationGCSE A*-C -4643.4 1304.3 -3.560
## EducationOther -4196.8 1732.4 -2.422
## EducationNo -4822.0 1955.0 -2.467
## SexFemale -6733.5 950.5 -7.084
## IndustryBanking, Finance 3323.9 1599.3 2.078
## IndustryPublic admin, education, health -304.0 1443.3 -0.211
## IndustryOther 5704.1 1408.0 4.051
## NumEmployeeUnder 500 852.8 930.4 0.917
## NumEmployeeOver 500 5710.0 1213.1 4.707
## OccupationProfessional -1061.2 1657.1 -0.640
## OccupationAssociate Professional, Technical -2819.2 1756.7 -1.605
## OccupationAdministrative, Secretarial -8265.5 1820.3 -4.541
## OccupationSkilled Trades -8147.8 1961.9 -4.153
## OccupationCaring, Leisure, Other Service -8917.5 1893.5 -4.709
## OccupationSales, Customer Service -11633.3 2068.8 -5.623
## OccupationProcess, Plant, Machine Operatives -12386.7 2232.6 -5.548
## OccupationElementary -14151.0 2031.1 -6.967
## MaritalMarried 1826.5 929.8 1.964
## MaritalOther 2238.0 1385.1 1.616
## ReligionYes -1139.6 860.2 -1.325
## EthnicityAsian -3553.5 2111.1 -1.683
## EthnicityBlack -1550.0 2522.3 -0.614
## EthnicityOther -285.9 2141.3 -0.134
## workRegionYorkshire and the Humber 1826.7 1614.9 1.131
## workRegionEast Midlands 1476.9 1930.2 0.765
## workRegionWest Midlands -3400.1 1879.2 -1.809
## workRegionEast of England 2152.1 2354.0 0.914
## workRegionLondon 2047.1 1635.5 1.252
## workRegionSouth West 1021.6 1713.9 0.596
## workRegionSouth East 1133.0 1544.5 0.734
## workRegionOutside UK 9102.3 9549.4 0.953
## Pr(>|t|)
## (Intercept) < 2e-16 ***
## EducationHigher Education 0.009435 **
## EducationA Level 0.000288 ***
## EducationGCSE A*-C 0.000406 ***
## EducationOther 0.015762 *
## EducationNo 0.013970 *
## SexFemale 4.69e-12 ***
## IndustryBanking, Finance 0.038183 *
## IndustryPublic admin, education, health 0.833252
## IndustryOther 5.89e-05 ***
## NumEmployeeUnder 500 0.359789
## NumEmployeeOver 500 3.24e-06 ***
## OccupationProfessional 0.522218
## OccupationAssociate Professional, Technical 0.109162
## OccupationAdministrative, Secretarial 7.01e-06 ***
## OccupationSkilled Trades 3.85e-05 ***
## OccupationCaring, Leisure, Other Service 3.21e-06 ***
## OccupationSales, Customer Service 3.10e-08 ***
## OccupationProcess, Plant, Machine Operatives 4.65e-08 ***
## OccupationElementary 1.00e-11 ***
## MaritalMarried 0.050024 .
## MaritalOther 0.106753
## ReligionYes 0.185834
## EthnicityAsian 0.092949 .
## EthnicityBlack 0.539165
## EthnicityOther 0.893841
## workRegionYorkshire and the Humber 0.258528
## workRegionEast Midlands 0.444550
## workRegionWest Midlands 0.070979 .
## workRegionEast of England 0.361025
## workRegionLondon 0.211267
## workRegionSouth West 0.551404
## workRegionSouth East 0.463538
## workRegionOutside UK 0.340953
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9206 on 509 degrees of freedom
## Multiple R-squared: 0.5031, Adjusted R-squared: 0.4709
## F-statistic: 15.62 on 33 and 509 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = Salary ~ Education + Sex + Industry + NumEmployee +
## Occupation, data = facQlfs)
##
## Residuals:
## Min 1Q Median 3Q Max
## -28168.4 -5330.9 716.9 5810.2 28070.7
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) 30965.20 1838.43 16.843
## EducationHigher Education -3962.11 1553.36 -2.551
## EducationA Level -4994.07 1306.26 -3.823
## EducationGCSE A*-C -4324.68 1288.09 -3.357
## EducationOther -3379.98 1701.91 -1.986
## EducationNo -4100.46 1953.10 -2.099
## SexFemale -7073.80 932.32 -7.587
## IndustryBanking, Finance 3754.20 1589.81 2.361
## IndustryPublic admin, education, health -36.14 1442.07 -0.025
## IndustryOther 5421.75 1406.48 3.855
## NumEmployeeUnder 500 897.30 924.66 0.970
## NumEmployeeOver 500 6050.89 1187.47 5.096
## OccupationProfessional -1197.35 1647.72 -0.727
## OccupationAssociate Professional, Technical -2698.83 1739.08 -1.552
## OccupationAdministrative, Secretarial -8411.84 1812.10 -4.642
## OccupationSkilled Trades -8381.08 1950.88 -4.296
## OccupationCaring, Leisure, Other Service -9424.12 1849.28 -5.096
## OccupationSales, Customer Service -11781.38 2042.65 -5.768
## OccupationProcess, Plant, Machine Operatives -12550.62 2227.49 -5.634
## OccupationElementary -14916.41 1974.74 -7.554
## Pr(>|t|)
## (Intercept) < 2e-16 ***
## EducationHigher Education 0.011035 *
## EducationA Level 0.000148 ***
## EducationGCSE A*-C 0.000844 ***
## EducationOther 0.047555 *
## EducationNo 0.036255 *
## SexFemale 1.51e-13 ***
## IndustryBanking, Finance 0.018571 *
## IndustryPublic admin, education, health 0.980016
## IndustryOther 0.000130 ***
## NumEmployeeUnder 500 0.332295
## NumEmployeeOver 500 4.86e-07 ***
## OccupationProfessional 0.467755
## OccupationAssociate Professional, Technical 0.121297
## OccupationAdministrative, Secretarial 4.37e-06 ***
## OccupationSkilled Trades 2.07e-05 ***
## OccupationCaring, Leisure, Other Service 4.85e-07 ***
## OccupationSales, Customer Service 1.38e-08 ***
## OccupationProcess, Plant, Machine Operatives 2.87e-08 ***
## OccupationElementary 1.90e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9295 on 523 degrees of freedom
## Multiple R-squared: 0.4795, Adjusted R-squared: 0.4606
## F-statistic: 25.35 on 19 and 523 DF, p-value: < 2.2e-16stargazer(list(facQlfs.lm1, facQlfs.lm2), digits = 2)##
## % Table created by stargazer v.5.2 by Marek Hlavac, Harvard University. E-mail: hlavac at fas.harvard.edu
## % Date and time: Thu, Oct 12, 2017 - 13:57:53
## \begin{table}[!htbp] \centering
## \caption{}
## \label{}
## \begin{tabular}{@{\extracolsep{5pt}}lcc}
## \\[-1.8ex]\hline
## \hline \\[-1.8ex]
## & \multicolumn{2}{c}{\textit{Dependent variable:}} \\
## \cline{2-3}
## \\[-1.8ex] & \multicolumn{2}{c}{Salary} \\
## \\[-1.8ex] & (1) & (2)\\
## \hline \\[-1.8ex]
## EducationHigher Education & $-$4,026.84$^{***}$ & $-$3,962.11$^{**}$ \\
## & (1,545.35) & (1,553.36) \\
## & & \\
## EducationA Level & $-$4,842.31$^{***}$ & $-$4,994.07$^{***}$ \\
## & (1,326.33) & (1,306.26) \\
## & & \\
## EducationGCSE A\textasteriskcentered -C & $-$4,643.45$^{***}$ & $-$4,324.68$^{***}$ \\
## & (1,304.35) & (1,288.09) \\
## & & \\
## EducationOther & $-$4,196.82$^{**}$ & $-$3,379.98$^{**}$ \\
## & (1,732.44) & (1,701.91) \\
## & & \\
## EducationNo & $-$4,822.00$^{**}$ & $-$4,100.46$^{**}$ \\
## & (1,954.95) & (1,953.10) \\
## & & \\
## SexFemale & $-$6,733.45$^{***}$ & $-$7,073.80$^{***}$ \\
## & (950.54) & (932.32) \\
## & & \\
## IndustryBanking, Finance & 3,323.91$^{**}$ & 3,754.20$^{**}$ \\
## & (1,599.34) & (1,589.81) \\
## & & \\
## IndustryPublic admin, education, health & $-$304.01 & $-$36.14 \\
## & (1,443.26) & (1,442.07) \\
## & & \\
## IndustryOther & 5,704.14$^{***}$ & 5,421.75$^{***}$ \\
## & (1,407.96) & (1,406.48) \\
## & & \\
## NumEmployeeUnder 500 & 852.78 & 897.30 \\
## & (930.38) & (924.66) \\
## & & \\
## NumEmployeeOver 500 & 5,710.04$^{***}$ & 6,050.89$^{***}$ \\
## & (1,213.08) & (1,187.47) \\
## & & \\
## OccupationProfessional & $-$1,061.17 & $-$1,197.35 \\
## & (1,657.11) & (1,647.72) \\
## & & \\
## OccupationAssociate Professional, Technical & $-$2,819.16 & $-$2,698.83 \\
## & (1,756.73) & (1,739.08) \\
## & & \\
## OccupationAdministrative, Secretarial & $-$8,265.49$^{***}$ & $-$8,411.84$^{***}$ \\
## & (1,820.32) & (1,812.10) \\
## & & \\
## OccupationSkilled Trades & $-$8,147.81$^{***}$ & $-$8,381.08$^{***}$ \\
## & (1,961.93) & (1,950.88) \\
## & & \\
## OccupationCaring, Leisure, Other Service & $-$8,917.46$^{***}$ & $-$9,424.12$^{***}$ \\
## & (1,893.52) & (1,849.28) \\
## & & \\
## OccupationSales, Customer Service & $-$11,633.34$^{***}$ & $-$11,781.38$^{***}$ \\
## & (2,068.85) & (2,042.65) \\
## & & \\
## OccupationProcess, Plant, Machine Operatives & $-$12,386.71$^{***}$ & $-$12,550.62$^{***}$ \\
## & (2,232.65) & (2,227.49) \\
## & & \\
## OccupationElementary & $-$14,151.02$^{***}$ & $-$14,916.41$^{***}$ \\
## & (2,031.08) & (1,974.74) \\
## & & \\
## MaritalMarried & 1,826.49$^{*}$ & \\
## & (929.78) & \\
## & & \\
## MaritalOther & 2,238.00 & \\
## & (1,385.06) & \\
## & & \\
## ReligionYes & $-$1,139.62 & \\
## & (860.22) & \\
## & & \\
## EthnicityAsian & $-$3,553.47$^{*}$ & \\
## & (2,111.13) & \\
## & & \\
## EthnicityBlack & $-$1,549.96 & \\
## & (2,522.35) & \\
## & & \\
## EthnicityOther & $-$285.90 & \\
## & (2,141.35) & \\
## & & \\
## workRegionYorkshire and the Humber & 1,826.66 & \\
## & (1,614.88) & \\
## & & \\
## workRegionEast Midlands & 1,476.86 & \\
## & (1,930.21) & \\
## & & \\
## workRegionWest Midlands & $-$3,400.14$^{*}$ & \\
## & (1,879.16) & \\
## & & \\
## workRegionEast of England & 2,152.12 & \\
## & (2,354.01) & \\
## & & \\
## workRegionLondon & 2,047.13 & \\
## & (1,635.53) & \\
## & & \\
## workRegionSouth West & 1,021.60 & \\
## & (1,713.94) & \\
## & & \\
## workRegionSouth East & 1,132.99 & \\
## & (1,544.45) & \\
## & & \\
## workRegionOutside UK & 9,102.29 & \\
## & (9,549.41) & \\
## & & \\
## Constant & 29,672.04$^{***}$ & 30,965.20$^{***}$ \\
## & (2,358.79) & (1,838.43) \\
## & & \\
## \hline \\[-1.8ex]
## Observations & 543 & 543 \\
## R$^{2}$ & 0.50 & 0.48 \\
## Adjusted R$^{2}$ & 0.47 & 0.46 \\
## Residual Std. Error & 9,205.64 (df = 509) & 9,295.25 (df = 523) \\
## F Statistic & 15.62$^{***}$ (df = 33; 509) & 25.35$^{***}$ (df = 19; 523) \\
## \hline
## \hline \\[-1.8ex]
## \textit{Note:} & \multicolumn{2}{r}{$^{*}$p$<$0.1; $^{**}$p$<$0.05; $^{***}$p$<$0.01} \\
## \end{tabular}
## \end{table}Null hypothesis for anova is that the mean(average value of the dependent variable) is the same for all groups
##
## studentized Breusch-Pagan test
##
## data: Salary ~ Education + Sex + Industry + NumEmployee + Occupation
## BP = 37.53, df = 19, p-value = 0.0068075. Discussion
5.1 What results did you find
5.2 Why is it interesting
5.3 What would be the next steps
6. References
Notes:
parallel plots message table for results anova analysis t-test tables mean table for each boxplot whether include age in linear regression